The Effect of Time Horizon and Time Scale on the Parameters Of the Quasi-Hyperbolic Discounting Model

Estimates of the parameters of the quasi-hyperbolic discounting model–beta and delta–have been used for quantitative purposes, including comparisons of the psychology of discounting between populations and decision-making contexts, design of optimal regulation, and adjustment of benefits in benefit-cost analysis. I show that estimates of both parameters are sensitive to unavoidable features of the estimation procedure: the time horizon (how far in the future the time periods used for estimation lie) and the time scale (whether time periods are defined in months, years, etc), and argue that as a result, quantitative estimates should be used with great caution, if at all. Using online survey data, I show that beta is decreasing in both time horizon and time scale, and vice versa for delta. The time-horizon effect appears to be the result of estimating a discontinuous discounting model using data that are generated by a continuous discounting process. The time-scale effect appears to be caused by a genuine difference across scales in how individuals discount. I discuss implications for positive and normative analysis, and discuss possible approaches to proceeding with quantitative analysis in the face of the fundamental invalidity of beta and delta as quantitative measures of psychological or physiological phenomena